The area of circle touching parabola $y=x^2$ at $(1,1)$ and having directrix of $y=x^2$ as its normal is $125 A \pi$, then $A$ is

If the 4th term in the expansion of $$\left(p x+\frac{1}{x}\right)^n, n \in N$$ is $$\frac{5}{2}$$ and three normals to the parabola $$y^2=x$$ are drawn through a point $$(q, 0)$$, then

If the tangent at $$P$$ on $$y^2=4 a x$$ meets the tangent at the vertex in $$Q$$ and $$S$$ is the focus of the parabola, then $$\angle S Q P$$ is equal to

The locus of a point which moves in a plane such that its distance from a fixed point in the plane is always equal to its distance from a fixed straight line in the same plane represents